This research started with an algebra for reasoning about rely/guarantee concurrency for a shared memory model. The approach taken led to a more abstract algebra of atomic steps, in which atomic steps synchronise (rather than interleave) when composed in parallel. The algebra of rely/guarantee concurrency then becomes an instantiation of the more abstract algebra. Many of the core properties ne...

Interpretation is a theory developed to reason about the abstraction relation between two different semantics. The theory requires the two semantics to be defined on domains which are complete lattices. (C, ) (concrete domain) is the domain of the concrete semantics, while (A,≤) (abstract domain) is the domain of the abstract semantics. The partial order relations reflect an approximation relat...

We provide a systematic in-depth study of the semantics of abstract dialectical frameworks (ADFs), a recent generalisation of Dung’s abstract argumentation frameworks. This is done by associating with an ADF its characteristic one-step consequence operator and defining various semantics for ADFs as different fixpoints of this operator. We first show that several existing semantical notions are ...